Is it possile to create a flat-color (shadeless) shader in Blender 2.83 that is also flat when in a reflection?
Flat Color

plug RGB node directly, there is no need to use Emission shader

Flat Color in Reflection with Roughness

math Light Path of Camera Ray with Glossy Ray** and use as factor in Mix Shader node

Shadow

current setup generates shadow, if you dont want that plug Transparent shader into top Shader socket of Mix Shader node.

For your Edit2: Delete your Diffuse Shader that generates indirect light on surrounding objects.


Great article to check How the light path node works